This paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

中文翻译：

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线性连续时间分数阶系统约束调节问题的优化方法

本文讨论了线性连续时间分数阶系统的约束调节问题（CRP）。目的是寻找分数阶系统CRP的线性反馈控制律的存在条件，并通过正不变集提供数值求解方法。在两种不同的初始状态约束条件下，获得了保证CRP存在线性反馈控制律的代数条件。提出了将多面体集设为线性分数阶系统的正不变集的充要条件，并基于多面体集的正不变性，提出了求解线性状态反馈控制律的优化模型和相应算法。所提出的模型和算法将分数阶CRP问题转换为线性规划问题，可以从计算的角度轻松解决该问题。数值算例说明了所提出的结果并显示了我们方法的有效性。